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Adding Vectors. Example of adding two vectors neither at right angles to one another nor on an x or y axis. The Process:. First draw the vectors on an x:y axis, showing them attached head to tail. Second, determine the x and y components of V1. Third, determine the x and y components of V2.

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Adding vectors l.jpg

Adding Vectors

Example of adding two vectors neither at right angles to one another nor on an x or y axis.


The process l.jpg
The Process:

  • First draw the vectors on an x:y axis, showing them attached head to tail.

  • Second, determine the x and y components of V1.

  • Third, determine the x and y components of V2.

  • Fourth, Add the x components of the vectors together.

  • Fifth, Add the y components of the vectors together.

  • Sixth, Use the sum of the x components as the x component of the resultant vector; Use the sum of the y components as the y component of the resultant vector.

  • Seventh, proceed to “add” the resultant’s x and y values.



Resolve the 1st vector into its x and y components l.jpg
Resolve the 1st vector into its x and y components.

V1y = V1 * Sin 60 or V1 * Cos 30 = 0.866 Km, N

V1x = V1 * Cos 60 or V1 * Sin 30 = 0.5 km, E


Resolve the 2nd vector into its x and y components l.jpg
Resolve the 2nd vector into its x and y components.

V2y = V2 * Sin 30 or V2 * Cos 60 = 1 Km, N

V2x = V2 * Cos 30 or V2 * Sin 60 = 1.732 Km, E


Next add the components l.jpg
Next, add the components.

V1y + V2y = 0.866 Km + 1.000 Km = 1.866 Km, N

V1x + V2x = 0.500 Km + 1.732 Km = 2.232 Km, E


Determine the resultant l.jpg
Determine the resultant:

1st use c^2 = a^2 + b^2

c = (a^2 + b^2)^(1/2)

c = [(1.866 km)^2 + (2.232 km)^2]^(1/2)

So c = 2.909 km

2nd use Angle = Inv Tan (Ry / Rx) = Inv Tan (1.886 km / 2.232 km) = 39.9 degrees; The direction is N of E.

So R (the resultant) is equal to 2.909 Km, 39.9 deg N of E

or 2.909 Km, 50.1 deg from N, or E of N


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